Optimal. Leaf size=18 \[ a^2 c x-\frac{1}{3} b^2 c x^3 \]
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Rubi [A] time = 0.0042267, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {41} \[ a^2 c x-\frac{1}{3} b^2 c x^3 \]
Antiderivative was successfully verified.
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Rule 41
Rubi steps
\begin{align*} \int (a+b x) (a c-b c x) \, dx &=\int \left (a^2 c-b^2 c x^2\right ) \, dx\\ &=a^2 c x-\frac{1}{3} b^2 c x^3\\ \end{align*}
Mathematica [A] time = 0.0016718, size = 18, normalized size = 1. \[ c \left (a^2 x-\frac{b^2 x^3}{3}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 17, normalized size = 0.9 \begin{align*}{a}^{2}cx-{\frac{{b}^{2}c{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02333, size = 22, normalized size = 1.22 \begin{align*} -\frac{1}{3} \, b^{2} c x^{3} + a^{2} c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.24425, size = 35, normalized size = 1.94 \begin{align*} -\frac{1}{3} x^{3} c b^{2} + x c a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.057572, size = 15, normalized size = 0.83 \begin{align*} a^{2} c x - \frac{b^{2} c x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05493, size = 22, normalized size = 1.22 \begin{align*} -\frac{1}{3} \, b^{2} c x^{3} + a^{2} c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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